Global asymptotic stabilization of nonlinear system with multiple singular points using changeover of control Lyapunov-Morse function

The purpose of this paper is to solve the global asymptotic stabilization problem of multi-input affine systems on general manifolds. It is known that if the control Lyapunov-Morse function (CLMF) satisfies some assumptions, the controlled system is globally asymptotically stablizable via the discontinuous feedback law derived from the CLMF. However, in some cases we cannot find CLMFs satisfying the assumption. In this paper, we perturb original CLMF and we change over the feedback laws derived from the original and perturbed CLMF under some rules. Moreover, a condition of global asymptotic stability of controlled system with feedback law is also obtained.